PennyLane is a Python 3 software framework for optimization and machine learning of quantum and hybrid quantumclassical computations. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware.We provide plugins for Strawberry Fields, Rigetti Forest, Qiskit, and ProjectQ, allowing PennyLane optimizations to be run on publicly accessible quantum devices provided by Rigetti and IBM Q. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, and autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.

We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized model such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the Strawberry Fields software library. These experiments, including a classifier for fraud detection, a network which generates Tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks. arXiv:1806.06871v1 [quant-ph]

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A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks. No photonic machine offering programmability over all its quantum gates has demonstrated quantum computational advantage: previous machines1,2 were largely restricted to static gate sequences. Earlier photonic demonstrations were also vulnerable to spoofing3, in which classical heuristics produce samples, without direct simulation, lying closer to the ideal distribution than do samples from the quantum hardware. Here we report quantum computational advantage using Borealis, a photonic processor offering dynamic programmability on all gates implemented. We carry out Gaussian boson sampling4 (GBS) on 216 squeezed modes entangled with three-dimensional connectivity5, using a time-multiplexed and photon-number-resolving architecture. On average, it would take more than 9,000 years for the best available algorithms and supercomputers to produce, using exact methods, a single sample from the programmed distribution, whereas Borealis requires only 36 μs. This runtime advantage is over 50 million times as extreme as that reported from earlier photonic machines. Ours constitutes a very large GBS experiment, registering events with up to 219 photons and a mean photon number of 125. This work is a critical milestone on the path to a practical quantum computer, validating key technological features of photonics as a platform for this goal.

We introduce Strawberry Fields, an open-source quantum programming architecture for light-based quantum computers, and detail its key features. Built in Python, Strawberry Fields is a full-stack library for design, simulation, optimization, and quantum machine learning of continuous-variable circuits. The platform consists of three main components: (i) an API for quantum programming based on an easy-to-use language named Blackbird; (ii) a suite of three virtual quantum computer backends, built in NumPy and TensorFlow, each targeting specialized uses; and (iii) an engine which can compile Blackbird programs on various backends, including the three built-in simulators, and -in the near future -photonic quantum information processors. The library also contains examples of several paradigmatic algorithms, including teleportation, (Gaussian) boson sampling, instantaneous quantum polynomial, Hamiltonian simulation, and variational quantum circuit optimization.

We study what is arguably the most experimentally appealing Boson Sampling architecture: Gaussian states sampled with threshold detectors. We show that in this setting, the probability of observing a given outcome is related to a matrix function that we name the Torontonian, which plays an analogous role to the permanent or the Hafnian in other models. We also prove that, provided that the probability of observing two or more photons in a single output mode is sufficiently small, our model remains intractable to simulate classically under standard complexity-theoretic conjectures. Finally, we leverage the mathematical simplicity of the model to introduce a physically motivated, exact sampling algorithm for all Boson Sampling models that employ Gaussian states and threshold detectors.arXiv:1807.01639v2 [quant-ph]

We study time ordering corrections to the description of spontaneous parametric down-conversion (SPDC), four wave mixing (SFWM) and frequency conversion (FC) using the Magnus expansion. Analytic approximations to the evolution operator that are unitary are obtained. They are Gaussian preserving, and allow us to understand order-by-order the effects of time ordering. We show that the corrections due to time ordering vanish exactly if the phase matching function is sufficiently broad. The calculation of the effects of time ordering on the joint spectral amplitude of the photons generated in spontaneous SPDC and SFWM are reduced to quadrature.

As a promising candidate for exhibiting quantum computational supremacy, Gaussian boson sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. In this work, we establish sufficient conditions for efficient approximate simulation of GBS under the effect of errors such as photon losses and dark counts. We show that efficient simulation of GBS is possible if the per-photon transmission rate scales as the inverse of the square root of the average number of photons. As a consequence, for architectures where losses increase exponentially with circuit depth, our results place an upper bound on circuit size beyond which GBS becomes simulable. We also find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to fight against photon loss.